The role of commitment in resource allocation: A laboratory

Unobservable commitment and management control: An experiment

Steven T. Schwartz*

Eric E. Spires**

David E. Wallin**

Richard A. Young**

July 2010

* Binghamton University

School of Management

SUNY - Binghamton University

Binghamton, NY 13902

607-777-2102 sschwartz@binghamton.edu

** The Ohio State University

Fisher 410

Columbus, OH 43210

614-292-0889 young_53@fisher.osu.edu

The authors thank Harry Evans, Brian Mittendorf, and Don Moser, as well as participants at the

Economic Science Association and Northeast AAA meetings and seminar participants at Binghamton

University for their helpful comments. Financial support of the Fisher College of Business is gratefully acknowledged.

Unobservable commitment and management control: An experiment

Abstract

We conduct an experiment designed to investigate whether unobservable commitment strengthens or weakens non-binding threats. The setting follows closely that found in prior budgeting experiments, consisting of a superior and subordinate who bargain over the funding of an investment project. In the first two treatments superiors are either required to make an unobservable commitment on their maximum funding level or required to wait for the subordinate’s request before making a funding decision. In the third treatment, which was administered after we collected data on the first two treatments, the choice is made endogenous; superiors can choose whether to make an unobservable commitment or learn the subordinate’s request before making a funding decision. We find that unobservable commitment, on average, whether assigned or chosen, weakens the superiors’ willingness to inflict costly punishment on subordinates and, in turn, subordinates eventually learn to be more aggressive in their requests for funds. For a subset of superiors in the endogenous choice treatment unobservable commitment appears to be used as a norm enforcement mechanism, however these superiors do not gain financially from their behavior. We find some evidence of “posturing” by superiors, in that superiors who set a lenient binding commitment will attempt to mitigate the impact by making aggressive non-binding threats. We conjecture that unobservable commitment decreases the emotional response to unfair behavior by subordinates, and that information asymmetry accentuates this effect because the superior is never quite sure what behavior was possible by the subordinate. One possible implication of our results is that in some circumstances it may be better for superiors to let their emotions have “free rein” if their goal is to convince subordinates of their willingness to retaliate against them for their seemingly excessive funding requests.

1. Introduction

There is a rich literature on the use of accounting information to mitigate agency issues (Baiman

[1990], Bushman and Smith [2001], Demski [1976], Demski and Feltham [1978]). It should not be surprising that accounting information has a prominent role in control functions as it is difficult to manipulate and it is already be produced for non-control reasons. Major insights have been gained from this research on optimal report format, contract length, report timing, and relative performance evaluation.

Until recently, agency models generally have assumed that the principal can fully commit to the use of accounting information without cost. However, in many circumstances, commitment is not costless or is even prohibited. Further, the contracts we often observe in practice are designed to be flexible in unforeseen circumstances rather than containing rigid commitment provisions. More recently the agency literature has begun to reflect the observation that commitments may be of a limited nature [Arya et al.

1997; Arya et al 2000; Demski and Frimor 1999; Feltham and Hoffman 2007]. Therefore, it would appear then that empirical investigations of limited forms of commitment are worthwhile as well.

We conduct an experiment designed to investigate a type of limited commitment wherein a superior can make an ex ante commitment that is not observable to a subordinate. Superiors typically have better access to corporate governance structures, outside funding agencies, and regulatory bodies, and may very well make informal yet binding commitments to these parties regarding future resource allocation. For example buyout parties in LBOS, such as private equity firms, are likely to ask for certain commitments from existing management regarding cost cutting or reductions in slack but understandably may not want to make their requirement public.

1 Therefore management may subsequently have their hands tied, but might not be able to credibly signal this to lower level employees. There is also a well developed literature in public finance on statutory fiscal constraints and assignments of monetary policy

1 See for example Burrough and Helyar [1990]) on the role of corporate spending and perquisite consumption in the negotiations surrounding the buyout of RJR Nabisco. For a more general discussion of the role of leveraged buyouts in controlling slack and perquisite consumption see Jensen [1986].

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that form a sort of opaque commitment that acts as a commitment device (Kumar and Ter-Minassian

[2007]). In consequence, politicians may enter truly into binding commitments, but it may be difficult for constituencies or even seasoned observers to understand the exact nature of the commitment.

2 Finally there is evidence that individuals use the restrictions in retirement savings vehicles as a method of commitment to not otherwise spend the money earlier (Laibson, Repetto and Tobacman 1998).

3 Therefore unobservable commitment seems to be often associated with issues related to budgeting and resource allocation at the national, corporate and individual level. In our experiment we focus on the effects of unobservable commitment to enforce non-binding threats in a stylized budgeting setting.

We undertake our study of unobservable commitment in the context of several models of capital investment; most relevant of these are Antle and Eppen [1985] and Arya et al. [1997]. The simplicity of the setting allows for a straightforward comparison of standard agency theory predictions and alternative behavioral theory predictions (Brown et al., 2009). The setting has all the necessary elements of an interesting agency problem yet has been simplified to include just a superior and a subordinate. The subordinate holds private information regarding the profitability of an investment project, owns no private resources and consumes any over-funding as slack. The superior has resources to fund the project and is its residual claimant. When commitment is free and publicly observable, the superior finds it optimal to commit to a maximum acceptable funding level, or limit . The limit is generally less than the proceeds from the investment, which implies the superior commits to turn down some profitable investments that would otherwise improve her welfare. Therefore, it is necessary for the commitment to be credible in order for it to be effective.

Several experiments have used this setting to investigate the role of commitment and nonpecuniary motivations. Evans et al. [2001] found observable commitment was better for the superior than

2 As an example, many state governors use the constitutional bans on deficit spending as arguments for pay freezes or cuts for state employees. However the extent to which the balanced budget provisions are truly binding and the extent to which citing them is a political bargaining tactic is difficult to ascertain in any particular case (Poterba

[1995]).

3 The idea here is that the commitment to retirement savings is non-strategic and simply binds one’s own hands.

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trust alone.

4 Rankin et al. [2003] found that observable commitment was better at reducing slack than superior discretion, but the effect on superior earnings was ambiguous. Rankin et al. [2008] found that superior discretion increased superior earnings relative to trust alone. We specifically build on the finding of Rankin et al. [2003] that when superiors make non-binding announcements prior to using their discretion it disciplines subordinates’ budget requests to a greater extent than discretion without the ability to make non-binding announcements. That is, the announcement of threats helps to mitigate control problems, even though superiors have no available commitment mechanism. However, subordinates eventually see through the threats and they then become less useful. We investigate whether unobservable commitment can strengthen the efficacy of non-binding announcements.

In all treatments the superior has the discretion, ex post, to reject requests but has no pecuniary incentive to do so. In the No Commitment treatment (NC), which served as a control, the superior could not make a binding commitment of any type. This treatment essentially replicates Rankin et al.’s [2003] study. In the Unobservable Commitment treatment (UC) the superior made an unobservable but binding commitment regarding the limit . After we administered the first two treatments, we added a third treatment, Endogenous Choice (EC), to better test the willingness of individuals to use the unobservable commitment as a commitment device in that the superior had the choice but not the obligation to use unobservable commitment.

We draw on several streams of literature to develop expectations of the effects of unobservable commitment. Individuals have shown reluctance to go back on their threats (Cialdini [1984]). Further, there is evidence that some individuals try commit to desired behavior if they believe they will be tempted to do otherwise in the future ( Bryan, Karlan and Nelson [2009]).

5 If so, unobservable commitment may be utilized by superiors to follow through on their threats to reject unfair requests. On the contrary, without the emotions that would otherwise accompany having just seen a subordinate act unfairly, superiors may

4 In this context, “trust alone” refers to a setting where the superior cannot reject the project.

5 An example would be people who buy clothes that are a size too small. Although these individuals can break their commitment, they are imposing a cost on themselves if they do not lose weight.

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be tempted to focus on wealth-maximization rather than norm enforcement when choosing their unobservable commitment. Some experiments have shown that contingent decisions made in advance tend to minimize norm enforcement (Blount and Bazerman [1996]).

Our primary finding is that, in general, when superiors make an unobservable commitment, either assigned or chosen, they are much less willing to enforce social norms than normally found in similar games or when they wait for the subordinate’s request. In particular, they commit to a high limit, implying a willingness to accept a small share of the project’s expected profits. For example, in the latter rounds, superiors in the UC treatment accept offers of ten percent or less of the expected profits 52% of the time, whereas participants in the NC treatment accept such offers only 14% of the time.

6 Somewhat similar results are found in EC when superiors choose to use unobservable commitment. However in EC, for the subset of superiors who use of unobservable commitment is moderate, tend to use it to enforce norms.

Interestingly, superiors, when given the choice, choose to make a commitment about 70% of the time. Subordinates in time learn to be more aggressive with their requests in all treatments. Finally, we observe that posturing takes place when unobservable commitment is assigned. By this, we mean that the more acquiescent superiors are in their unobservable choice of the limit, the more threatening they are in their non-binding announcement of their intended limit.

We conjecture that our results are due to the lack of visceral emotions present when superiors make their unobservable commitments. This effect is likely exacerbated by the information asymmetry between superior and subordinate resulting in the superior never being sure what exactly is fair in a given situation. Therefore, we conclude that it may be better for superiors to let their emotions play a role in responding to subordinates’ behavior, in order to make their threats more believable.

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6 In comparison, Rankin et al. [2003] found that in their observable commitment setting offers of 10% of the expected surplus or less were accepted less than 1% of the time.

7 There is a significant literature on emotions as an enforcement mechanism. See for example Hirschleifer (1987),

Frank (1988) and Fehr and Gächter (2000).

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The structure of this paper is as follows. Section 2 describes the experiment. Section 3 develops the hypotheses. Section 4 presents the results for treatments NC and UC. Section 5 presents results for treatment EC. Section 5 provides a summary and conclusion.

2. Description of Experiment

Participants were students recruited from undergraduate business classes at a large

Midwestern university. All treatments were administered in two sessions, with sessions of 20 and 18 participants in NC and UC and two sessions of 20 participants for EC. The experiment consisted of four training rounds and twenty cash-earning rounds. The participants were randomly assigned a role, described to them as “Player A” or “Player B” that they held until the experiment was finished. (For expositional clarity, in the paper we continue to use the terms superior and subordinate, respectively.)

After each round participants were randomly re-matched, to simulate a one-shot setting but allow for a more efficient collection of data. Participants interacted over a computer network. Before administration, all participants were required to accurately complete a quiz on the rules and structure of the experiment.

In each round a superior had the decision rights to an investment project. The project’s cost was uniformly distributed on {0, 1, . . ., 200}.

8 If the project was funded, the superior received experimental points equal to the revenue of 200 minus the subordinate’s request and the subordinate received experimental points equal to the difference between the request and the actual cost. If the project was not funded the superior and subordinate received zero from their interaction. However, the subordinate always received a wage of 25 experimental points per round from the experimenter, regardless of whether the project was funded.

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8 Before the experiment was administered cost vectors were drawn so as to accommodate a large potential number of participants, with each vector containing twenty i.i.d. random variables, one for each round. The first nineteen vectors were used in the two treatments, and so each treatment utilized the same random sample of 380 costs. The costs were drawn exactly as described in the instructions and were not censored. The sample (population) mean and standard deviations were 100.41 (100) and 56.15 (57.74), respectively.

9 Given our parameters, the fixed payment of 25 made to the subordinates would equalize superior and subordinate earnings, were the superiors to set the limit equal to the optimal observable commitment limit, as prescribed in

Antle and Eppen [1985].

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The superior moved first by announcing an intended limit to the subordinate. The subordinate observed the announcement from the superior and the actual cost of the project and then made a request to the superior. The request had to be greater than or equal to the actual cost and less than or equal to 200. In the UC treatment, the superior was required to make a binding commitment to a limit at the same time she announced her intended limit . The committed-to limit was never revealed to the subordinate, though the subordinate was aware a binding commitment had been made. The experimenter then implemented the superior’s project funding decision, given the subordinate’s request. In the NC treatment the superior made her funding decision ex post , after she received the subordinate’s request. In the EC treatment the superior chose whether to make an unobservable binding commitment prior to receiving the subordinate’s request or waiting to make her funding decision after receiving the request. Experimental points were converted to cash at a rate of $.02 US for each experimental point, and were accumulated throughout the experiment. Participants were assigned randomly to one session, and earned an average of approximately

$21 per 90-minute session. Participants were paid in private, outside the room where the experiment was conducted.

In the unique Nash equilibrium the superior accepts any cost that leaves her with positive earnings. Even if the subordinate believed the superior’s threat to reject some profitable projects, a wealth-maximizing superior should never actually commit to do so. Therefore, in expectation, the subordinate receives 100 and the superior receives 0 from the investment. However, extensive experimentation in structurally similar games indicates that the Nash equilibrium is unlikely to obtain.

3. Hypothesis Development

Structurally our experiment is similar to ultimatum games with one-sided uncertainty regarding the amount of surplus (Mitzkewitz and Nagel [1993], Croson [1996], Guth et al. [1996], Guth and Huck

[1997], Rankin et al. [2003, 2008], Rapoport and Sundali [1996], Schmitt [2004]). In this variation of the ultimatum game the size of the surplus is unknown, but its distribution is common knowledge. The proposer privately learns the realized surplus and offers an amount weakly less than the surplus to the

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responder. In these games responders reject offers involving less than 20% of the expected surplus about

40% of the time, while offers above 20% of the expected surplus are highly likely to be accepted (e.g.,

Condition 1 in Rapoport and Sundali [1996]). Our experiment differs from the basic ultimatum experiment in that it investigates the interplay between non-binding threats and binding but unobservable commitments.

There are three strands of the literature that are particularly relevant to our study: promises and threats, commitment devices, and the strategy method. We briefly summarize this literature below.

There is substantial evidence that individuals do not want to violate their promises and threats

(Charness and Dufwenberg [2006], Irlenbusch [2004]). Klein and O’Flaherty [1993], when describing some of the work done in this area, note, “We have an emotional response that tells us to follow through on our declarations, if tested. Talk is not always cheap .” Specifically, the promises and threats we refer to are conditional in nature; they indicate actions that will be taken in response to the prior actions of others which differentiates the communications we refer to from simple declarations such as intended in the

Battle-of-the-Sexes game. Of particular interest is the model and experiment of Ellingsen and

Johannesson [2004], who conclude that individuals’ resolve to follow through on their threats is strengthened if doing so leads to a fairer outcome; conversely, it is weakened if it leads to a less fair outcome. Therefore, individuals would want to follow through on those threats that in expectation would lead to fairer outcomes.

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Bryan, Karlan and Nelson [2009] review and synthesize the literature on commitment and argue there is growing evidence that there is a demand for “commitment devices” and that they affect behavior.

By commitment devices they refer to behavior meant solely to affect that person’s behavior. The literature tends to focus on temptation situations, such as smoking, overeating or overspending. The public finance literature also uses the term commitment device to describe the various fiscal restraint mechanisms that are enacted by governments in order to control spending (Debrun et al.

2008). The common theme in both

10 Other papers in this stream include Charness and Dufwenberg [2008a], Charness and Dufwenberg [2008b] and

Vanberg [2008].

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literatures is that the devices make it difficult to deviate from “desired” actions but are not necessary for the desired actions to be taken. Examples from public finance would be the PAYGO system in effect in the U.S from 1990 to 2002 and the euro-zone Stability and Growth Pact (Debrun and Kumar [2007],

Fuller [2009]). Under both these regimes politicians “commit” to behavior they are free to carry out in any event.

11 A similar behavior is found in individuals’ budgeting behavior with respect to retirement savings. Individuals have been found to value the restrictions on early use of retirement savings. The benefits are clearly framed as a matter of self-control and not as part of strategy to influence others

(Laibson et al. [1998]).

Of course, given that individuals are free to follow through on their intentions without commitment devices, it is natural to question the value of commitment devices. Gul and Pesendorfer

[2001] take the approach that individuals derive utility from the menu of choices as well as their actual choice. As an example, an individual might choose to have a hamburger over a vegetarian meal at lunch if both options are available. However, that same individual would be happier to have the choice of hamburger removed. Therefore, they would rationally choose to go to a vegetarian restaurant, essentially committing to the vegetarian meal.

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Finally there is a stream of literature that examines the effect of games played using the strategy method (Selten [1967]). In an ultimatum game played under the strategy method, the responder specifies his or her response to every possible proposal without observing an actual proposal.

13 Although our setting is a bit different in that superiors choose a limit, ensuring monotonicity in their response, the basic

11 Admittedly in political settings one purpose of the commitment device might be to convince the electorate you have no choice but to abide by the “commitment.” However the exact commitment being made is rather opaque to the public; rules can be bent or changed as happened with the Stability and Growth Pact in 2005 (Calmfors

[2005]). So it is not clear that influencing the electorate is either an intended or effective motivation of fiscal restraints. Therefore these statutory restraints are similar in spirit to other commitment devices in that they voluntary erect barriers to breaking one’s commitment.

12 Another approach is taken in Gul and Pesendorfer [2008] based on time varying preferences.

13 When laboratory data are collected using the strategy method, the participant is in a sense being asked to make an unobservable commitment as to his future behavior, contingent on others’ choices. One advantage of the strategy method is it allows experimenters to gather more data within a given amount of time.

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attributes of the strategy method are in place with unobservable commitment.

14 Experiments comparing behavior with the strategy method relative to the more frequently employed iterated response method have found mixed results. Brandts and Charness [2000] found that punishment in a sequential “chicken game” was almost identical in the strategy and iterated response methods. Similarly, Oxoby and McLeish

[2004] found that behavior using the strategy method did not significantly differ from that obtained when using the iterated response method in an ultimatum game. Hannan, Rankin and Towry [2010] in setting very similar to ours, though without non-binding announcements, administered the iterated response method for four periods and then the strategy method for four periods. That is, the manipulation was within-subjects. They found slightly less leniency with the strategy method but did not provide any statistical tests.

In contrast, studies by Blount and Bazerman [1996] and Brosig et al. [2003] found that punishment by second movers under the strategy method was significantly less than that occurring under the iterated response method. Blount and Bazerman [1996] conjecture that under the strategy method participants focus on how different strategies affect their own payoffs, and are less concerned about how their payoffs compare to those of their opponent for each strategy. A somewhat different explanation is offered by Brosig et al. [2003], who conjecture that visceral emotions needed for costly punishment are not present when using the strategy method. Further, they cite evidence that indicates individuals are poor forecasters of their own future emotions. The latter two experiments suggest that unobservable commitment will lead to more lenience towards subordinates.

Subordinate behavior might also be affected by superiors’ unobservable commitments. Winter and Zamir [2005] find that in ultimatum games proposers adapt their behavior to the responders’ decisions. Extrapolating to our experiment, if unobservable commitment leads superiors to exhibit more lenient behavior, whereby they accept higher requests, subordinates would increase their requests over

14 For example, monotonicity was not imposed in Mitzkewitz and Nagel [1993], meaning a responder could commit to accept an offer of x and commit to reject an offer of x + a , where a > 0. However, the use of such strategies was rare.

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time. On the other hand, if UC superiors use the unobservable commitment to “lock in” their desire not to accept high requests, UC subordinates will reduce their requests over time.

Finally, we consider the effect of our manipulations on the non-binding announcements. Rankin et al. [2003] find that non-binding announcements have a strategic purpose, as opposed to simply revealing the superior’s fairness preferences. Therefore, superiors must trade off the believability of the threat (not make it too harsh) with the benefit of the threat (not make it too lenient). If we assume that the believability of the threats is the same in each of the treatments, we would expect the threats themselves to be the same. To the extent that the threats are more believable in one treatment than another we would expect harsher threats in the former than in the latter, but we have not developed such expectations.

First we consider treatments NC and UC. We develop arguments for why unobservable commitments would have an effect on the superior’s leniency towards the subordinate. On the one hand, we note that UC superiors may wish to bind themselves to follow through on their threats to reject projects, which they otherwise might be tempted to accept ex post . If the non-binding announcements are, on average, the same in each treatment, acceptance rates would be lower in UC than in NC and, ultimately, subordinate funding requests will be lower in UC than in NC. On the other hand, prior evidence suggests that decisions made before the others’ decisions are known tend to lead to more wealthmaximizing and less fairness-oriented behavior. Therefore, UC superiors may be willing to accept higher requests from subordinates. In this case, acceptance rates would be higher in UC than in NC and funding requests would eventually be higher in UC than in NC. The interplay between acceptance rates and funding requests wil determine the effects of NC and UC on superior and subordinate earnings.

Hypotheses for UC and NC are stated below in their null form.

H1: Acceptance rates will be the same in the UC and NC treatments.

H2: Funding requests will be the same in UC and NC treatments.

H3: Superiors’ earnings will be the same in the UC and NC treatments.

H4: Superiors’ earnings will be the same in the UC and NC treatments.

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H5: Non-binding announcements will be the same in the UC and NC treatments.

4. Results for Treatments UC and NC

Table 1 provides summary statistics for the experiment. As might be expected, superiors fare worse and subordinates fare better than in the observable commitment solution based on Antle and

Eppen (1985). Also the commitments are much higher than the observable commitment solution. The data are explored in more detail below.

[Insert Table 1 about here.]

4.1 Acceptance decisions (H1)

H1 in null form states that acceptance rates will be the same in the UC and NC treatments. We presented arguments that unobservable commitment may either strengthen or weaken the superior’s resolve to reject high funding requests. Our test is meant to provide evidence regarding which, if any, of these arguments holds true. As noted above, similar bargaining games have found that offers of above

20% of the expected surplus have high acceptance rates. Therefore, we focus our attention on requests that leave the superior with 20% or less of the expected profits; that is, requests of 180 and above. We partition the data into “low” and “high” requests (below 180 and above 179, resp.), and further partition the high requests into two partitions consisting of requests from 180 to 189 and above 189. Table 2 presents the percent of requests funded by treatment, by experiment half, and by request amount.


Even with participants who are well trained in the experimental procedure, it often takes several rounds before equilibrium behavior emerges. Table 2 shows some differences between the first and second halves of the experiment; therefore, we track the superiors’ acceptance rates over time and place more faith in results related to the later rounds. Figure 1 plots by pairs of rounds the acceptance rates for requests above 179 (because of small numbers of observations in some rounds, we aggregate into pairs).

The acceptance rate increased by an average of 4.73 percentage points for every two rounds for UC,

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compared to a slight decrease (1.45 percentage points) for NC. Beginning in rounds 7-8, UC always had a higher acceptance rate.

[Insert Figure 1 about here.]

To test H1 we estimate coefficients for the logit model in (1) using generalized estimating equations to control for the lack of independence of observations from the same superior (Zeger and

Liang [1986]):

Acceptance = α + β

1

(NC/UC) + β

2

(Round) + β

3

(NC/UC*Round) + ε, (1) where Acceptance is a dichotomous variable indicating whether a project was accepted (0 = not accepted;

1 = accepted), NC/UC is a dummy variable (0 for NC and 1 for UC) and Round represents pairs of rounds

(labeled 1 through 10).

15 The interaction term provides a test of the difference in slopes in Figure 1. The fitted model is given in (1′):

Expected Acceptance = 0.06 – 0.81 (NC/UC) – 0.03 (Round) + 0.20 (NC/UC*Round). (1′)

β

1

= –0.81 indicates that high-request acceptance rates for NC were lower than for UC in early rounds, but the difference is not significant (p < 0.15) 16 . The small negative β

2

indicates that acceptance rates for NC declined weakly over rounds; the decline is not significant (p > 0.60). The interaction coefficient, β

3,

is positive and strongly significant (p = 0.022), indicating that the high-request acceptance rates for UC increased across rounds at a greater rate than for NC. (For UC, the coefficient on Round is significantly positive, p < 0.01).

Although the logit indicates that high-request acceptance rates increased faster for UC than for

NC, it does not directly address whether the acceptance rates were significantly higher for UC. As shown in Table 2, considering all rounds, acceptance rates for high requests (> 179) were greater for UC than

NC, 57% versus 47%. This difference, however, is not significant (two-tailed p = 0.21 using a logit model

15 We used the GENMOD procedure in SAS, treating all observations for the same participant as a repeated measure for that subject. Unless otherwise noted, we use the same method on all tests to control for lack of independence within participants (superiors or subordinates depending on the dependent variable).

16 All reported p-values are two-tailed.

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similar to (1) but including only the NC/UC independent variable), most likely due to the lower acceptance for UC in early rounds. A similar test on the acceptance rates for the second half only (64% versus 46%) is marginally significant at two-tailed p < 0.10. The breakdown of the high requests indicates that the difference between NC and UC occurs primarily in the very high requests, those exceeding 189.

For these requests, the UC acceptance rate of 42% is significantly greater than the NC rate of 16% for all rounds (two-tailed p < 0.003) and the difference is even greater in the second half (52% versus 14%, p <

0.001). In the 180-189 request range, the NC acceptance rate was insignificantly higher than UC’s rate in the first half (p > .30), but this reversed in the second half (p > 0.20), consistent with UC superiors becoming more lenient than NC superiors over time. H1 is thus rejected; for high funding requests, especially in the latter rounds of the experiment, acceptance rates are significantly higher for UC than for

NC, and UC superiors become significantly more lenient than NC superiors over time.

4.1.1 Acceptance commitments

The binding commitment levels chosen by UC superiors can be viewed as intent to accept.

Table 3 presents frequency distributions of the binding commitments as well as descriptive statistics.

Two aspects of the data stand out. First, in UC there is an almost-unheard-of willingness of superiors to accept virtually anything from subordinates. In fact, in both halves of the experiment superiors committed to accept any request, even one yielding zero profits, approximately one-third of the time.

Second, there was an increase in superior acquiescence between the first and second half of the experiment. In the first half 24% of the commitments were for limits less than 170. In the second half only 9% of the commitments were for limits less than 170. The mean commitment significantly increased from 179.7 to 187.9 (two-tailed p < 0.01); a commitment of 187.9 secures only 11.4% of the conditional expected profits from investing (200-187.9)/(200 - 187.9/2)).


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4.2 Funding requests (H2)

H2 in null form states that funding requests will be the same in the UC and NC treatments.

Similar to H1, we presented arguments that unobservable commitment might either increase or decrease request levels, and that subordinates would “best-respond” to the behavior of superiors. Of course, we naturally anticipate that the cost realization as well as the treatment will affect the request. In addition, the superior’s nonbinding announcement may impact the subordinate’s request. To test H2 we estimate coefficients for the regression model in (2):

Request = α + β

1

(NC/UC) + β

2

(Costsq) + β

3

(NBA) + β

4

(Round) + β

5

(NC/UC*Round) + ε, (2) where NC/UC is a dummy variable (0 for NC and 1 for UC), Costsq is the actual cost squared (and divided by 1,000) 17 , NBA is the non-binding announcement, and Round is pairs of rounds (1 through 10).

We expect the effect of the treatment to differ by cost range as found in Rankin et al. (2003), so we estimated two models, one for costs above 100 and one for costs at or below 100. A significant treatment effect existed for high costs but not for low costs. This is not surprising, because the main difference in superior behavior between treatments involves their reaction to very high requests. When the cost is low, there is no reason for subordinates to “push the envelope” with a very high request; there is simply too much to lose from a rejection. Only when the underlying cost is high are there incentives for subordinates to make very high requests. The estimated model for costs above 100 is given in (2′):

Expected Request | High Cost = 130.82 – 8.32 (NC/UC) + 1.57 (Costsq) + 0.05 (NBA) + 0.40 (Round)

+ 1.61 (NC/UC*Round). (2′)

The positive coefficient on the interaction term (two-tailed p < 0.01) indicates that UC subordinates increased their funding requests at a faster rate than NC subordinates. Coupling this with the negative coefficient on the NC/UC dummy variable (two-tailed p < 0.10), we infer that in early rounds subordinates were more cautious in UC than in NC, but as subordinates in UC realized superiors were

17 There is a quadratic relation between cost and Request; therefore we use Costsq in the model. The inclusion of a linear component adds nothing. Costsq is divided by 1,000 to reduce the number of significant digits to be reported.

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becoming more acquiescent they became more daring, increasing their requests. For example, the predicted request for a cost of 150 and a non-binding announcement of 100 for UC (NC) in rounds 1&2 is

168 (172) whereas in rounds 19&20 it is 183 (175).

Figure 2, which focuses on high requests (> 179), provides further evidence on H2. It shows that the frequency of high requests is roughly the same between NC and UC in early rounds, but increases dramatically and significantly (two-tailed p < 0.02) for UC relative to NC in later rounds. Starting in rounds 7&8, UC subordinates always have a greater frequency of high requests than NC subordinates, which parallels the acceptance behavior of UC superiors (see Figure 1). These data for UC are consistent with the findings of Winter and Zamir [2005], who found that proposers maximize their earnings by adopting their behavior to responders’ decisions. H2 is rejected; funding requests for costs greater than

100 increase across rounds at a greater rate for UC than NC and are greater for UC than NC in later rounds.


4.3 Superiors’ earnings (H3)

H3 in null form states that superiors’ earnings will be the same for UC and NC. Results for H1 indicated that UC superiors accepted high requests more often than NC superiors, especially in later rounds. (In addition, for low requests UC acceptance rates were slightly higher than NC rates; see Table

2.) In testing H2, we found that UC subordinates made higher requests than NC subordinates, especially in later rounds. The increased level of requests and increased acceptance of the higher requests have opposite effects on superior profits. Tests of H3 can therefore be viewed as determining which effect prevailed for superiors.

Table 1 shows that superior earnings for NC are slightly lower in the first half than for UC (42.2 versus 45.4), slightly higher in the second half (32.5 versus 30.1), and approximately the same for all rounds. A repeated-measures model regressing superior earnings on NC/UC , Round (i.e., round-pairs), and NC/UC*Round shows no significant differences for either of the NC/UC -related variables, but a

15

significant Round effect (coef = -2.16, p < 0.001 for NC and -3.10, p < 0.001 for UC), indicating that superior profits decreased for both treatments over time at approximately the same rate. H3 is thus not rejected; earnings do not significantly differ between UC and NC superiors. The increased acceptance in

UC was counteracted by the subordinates’ increased requests.

4.4 Subordinates’ earnings (H4)

Analyses thus far indicate that UC superiors have higher acceptance rates than do NC superiors, subordinates increase their requests in response to this increased acceptance, and superiors do not benefit in terms of increased earnings. We therefore predict that subordinate profits will increase over rounds and at a faster rate for UC than NC. A repeated-measures model regressing subordinate earnings on NC/UC ,

Round (i.e., round-pairs), Costsq and NC/UC*Round shows that subordinate earnings increase over time for both NC (p < 0.07) and UC (p < 0.001), and at a faster rate for UC than NC (p < .03). H4 is rejected.

4.5 Non-binding announcements (H5)

Although Rankin et al. [2003] show that the non-binding announcements are, to a large extent, bluffs, they found that the announcements were somewhat informative about superiors’ willingness to fund requests. If this were to hold in our experiment, higher non-binding announcements would be associated with higher binding commitments in the UC treatment. To test this we estimated the regression in (3):

Expected Binding = 205.03 – 0.37 (NBA) – 1.50 (Round) + 0.04 (NBA*Round), (3) where Binding is the unobservable binding commitment and NBA is the non-binding announcement.

Contrary to expectations, NBA

’s coefficient is negative and significant (p < 0.02). In addition, the coefficient on NBA*Round is moderately significantly positive (p < 0.10).

18 That is, lower announcements were associated with higher unobservable binding commitments in early rounds of the experiment, but the effect becomes smaller over rounds until it does not exist in approximately round 19. The most

18 Binding clearly increases over rounds (see Table 3); the negative coefficient on Round (p > 0.40), however, in conjunction with the positive coefficient on NBA*Round , produces increasing Expected Binding over rounds.

16

straightforward explanation is that UC superiors were “posturing” — not simply bluffing, but actually trying to mitigate the impact of their planned acquiescence by making aggressive non-binding announcements. As an analogous test for the NC treatment, we used a binary dependent variable, whether a request was accepted, in a logit model with the same explanatory variables with the addition of a variable for request. The coefficient on NBA is positive (0.05, p < 0.001) and the coefficient on

NBA*Round is negative (-0.004, p < 0.04). This combination of coefficients indicates that in NC, no posturing was occurring in early rounds and the effect, although becoming smaller over rounds, lasts through all rounds. Thus, for NC, results for NBA are consistent with Rankin et al.’s [2003].

If wealth-maximizing UC subordinates see through the superiors’ use of the threat, subordinates would condition their request on non-binding announcements differently in NC than in UC. To address this conjecture we augmented model (2) to include an interaction term between NBA and NC/UC and estimated the model using all costs, given in (4):

Expected Request = 116.00 – 0.59 (NC/UC) + 1.50 (Costsq) + 0.15 (NBA) + 1.91 (Round)

– .05 (NC/UC*NBA) + 1.04 (NC/UC*Round). (4)

As expected from Rankin et al. [2003], the coefficient on NBA is positive and significant (p < 0.001), but the coefficient on NC/UC*NBA is not significant (p > 0.50).

19 Therefore, one might conclude that posturing was a rational strategy for superiors in UC, as it had a small beneficial effect on subordinates’ requests.

5. EC Treatment

After observing results in the first two treatments we administered the EC treatment as a more direct test of the decision to use commitment devices. In theory commitment devices are useful in order to avoid some sort of temptation. The temptation we consider is violating one’s threat not to fund high requests by subordinates. However after observing the results in the first two treatments it would seem

19 A separate model for the UC treatment shows that the coefficient on NBA of 0.10 (i.e., 0.15 – 0.05) is only marginally significant (two-tailed p < 0.11), but as indicated in the text, the UC NBA coefficient does not differ significantly from the NC NBA coefficient.

17

inappropriate to hypothesize behavior in accordance with the commitment device literature. Therefore we view this treatment as somewhat exploratory. Our general approach is to assess differences in behavior conditional on decision method choice.

5.1 Use of Unobservable Commitment

Table 4 presents results for the EC treatment. Superiors chose unobservable commitment in about

70% of rounds, while choosing not to use the commitment device in the other 30%. There is not a trend over time; the correlation between round and % usage of unobservable commitment is an insignificant -

0.07 and Table 4 shows that the superiors have virtually the same split in both halves. Our results stand in contrast to Paulsen and Roos [2010] and Paulsen and Tan [2007] who find players tend choose the option of viewing their opponents move before taking their action, when such choice is unobservable. In particular Paulsen and Roos [2010] use a Nash bargaining game (which is similar in most respect to an ultimatum game) and find that responders overwhelming choose view the proposer’s action before taking their own action, if proposers will never learn their viewing choice. For those who use “unobservable commitment” their actions are aggressive, not acquiescent. Notably, both Paulsen and Roos [2010] and

Paulsen and Tan [2007] have no privately informed players.


5.2 Acceptance rates for EC (H6 and H7)

Table 5 displays acceptance rates conditional on request. The pattern is similar to that in the first experiment. In particular, considering all rounds, EC-UC superiors accepted a higher percentage of high requests (> 179) than did EC-NC superiors (56% versus 53%). Also as in the first experiment, the largest differences occurred for very high requests such that more than 50% of the requests over 189 were accepted by EC-UC superiors in the second half. We estimated a logit model similar to (1) for high requests; the results are given in (5):


Expected Acceptance = -0.16 – 0.61 (NC/UC) + 0.04 (Round) + 0.12 (NC/UC*Round). (5)

18

No coefficient in (5) is significant (p > 0.30). Therefore there is no evidence of differences in high-request acceptance rates for EC-NC and EC-UC, unlike results in the first experiment. However, in

EC, superiors could choose whether or not to use UC; analyses considering the choices may be more informative in investigating our main issue, which is the nature of how superiors use UC, if at all, to avoid temptation. To address this, we divided the superiors, based on the amount and pattern of their usage of UC, into three groups: (1) strong revealed preference for NC, (2) strong revealed preference for

UC, and (3) no revealed preference. Specifically, if superiors had greater than 2/3 usage of either NC or

UC and late in the experiment had a string of 10 or more rounds of NC or UC, they were classified as

“revealing a strong preference.” Otherwise, they were classified as having no revealed preference. This resulted in 9 (2) superiors revealing a preference for UC (NC) and 9 superiors revealing no preference.

20

The average UC usage for superiors in the no preference group was 60.6%, whereas it was 90.6% (15%) in the UC (NC) preference group.


Table 6 displays acceptance rates conditional on requests for the three groups of superiors.

There are no significant differences between halves, so we report only for all rounds. Because there are so few observations for the NC preference, we confine our analysis to the UC and no preference groups. Figure 3 plots high-request acceptance rates over round-pairs for three groups: (1) “UC preference” who chose to use UC (UCpref-UC), (2) “no preference” who chose to use UC (nopref-

UC) and (3) “no preference” who chose to use NC (nopref-NC). There are small numbers of observations for some of the points.


It is readily apparent that the groups used UC differently for the high requests. The UCpref-

UC group’s line in Figure 3b is basically flat (slope = 0.28) and the acceptance rates are uniformly

20 We classified one superior as having a strong preference for UC even though the 10-round-string criterion was not met. This superior used UC for 90% of the rounds, but used NC for round 14 (and round 5), which resulted in an

8-round and 6-round string of UC late in the experiment.

19

higher than the other two groups’ rates. Table 6 shows that the UCpref-UC group accepted a remarkable 81% of the high requests. In stark contrast, the nopref-UC group accepted only 19% of high requests, and Figure 3b shows that the acceptance rates are uniformly lower than the others’ across all rounds. The nopref-NC group’s line has the greatest slope (5.58), indicating that this group became more lenient over time compared to the others (and of course they had more room to become lenient), but even so, by the end of the experiment their acceptance rates were not as high as the

UCpref-UC group’s.

21

We estimated three logit models like (1) for these groups, with each model comparing two groups. If the Round coefficient was not significant, we reran the model with only the NC/UC variable.

There is a strong NC/UC effect (p < 0.001) in the direction that high-request acceptance rates for nopref-

NC (61%, see Table 6) are higher than for nopref-UC (19%). This tendency is consistent across rounds. It appears that nopref superiors are indeed using the UC device to control their temptation not to carry through on their threat.

In addition, NC/UC for the UCpref-UC versus nopref-UC comparison was strongly significant (p

< 0.01), indicating that the UCpref group’s acceptance rates for high requests when choosing UC (81%) was higher than the nopref group’s rates when choosing UC (19%) and the effect is consistent across all rounds of the experiment. Clearly, the UCpref group was using the UC device differently than the nopref group.

In Figure 4, we focus on the use of UC and include data from the first experiment. To perform tests without resorting to cells with small numbers of observations, we analyze differences in the use of

UC for low and high requests. If superiors use UC to avoid their temptation to accept high requests, there will be substantial differences between the acceptance rates for low and high requests. Figure 4 plots the second-half data 22 for four groups of superiors: (1) all superiors in EC (ENDO-all), (2) superiors in EC

21 For nopref-NC, rounds 11&12 have one observation and rounds 13&14 have three observations, so these points should be viewed as having large sampling error.

22 Using data from all rounds would not make an appreciable difference.

20

who had no strong preference (ENDO-nopref), (3) superiors in EC who had a strong preference for UC

(ENDO-UCpref) and (4) superiors in the first experiment who were assigned to the UC treatment (EXO-

UC imposed). Note that groups (2) and (3) are subsets of group (1).


Because of the large impact of request on acceptance, all the lines are negatively sloped. To assess whether superiors used UC differently in controlling their temptation, we compared the slopes of ENDO-nopref and ENDO-UCpref; the ENDO-no pref slope is significantly more negative (twotailed p < 0.018). The ENDO-nopref group was successful in using UC to avoid the temptation to accept high requests; in fact, their behavior when they chose not to use UC (wherein they accepted

61% of high proposals, see Table 6) indicates that this group of superiors could not avoid the temptation without using UC. The superiors who preferred to use UC, on the other hand, accepted an extremely high percentage of high proposals. Their preference for using UC, therefore, must have been for reasons other than controlling their temptation.

It is instructive to compare the slopes between EXO-UC imposed and ENDO-all. These slopes are virtually the same, which indicates that the “average” behavior with respect to the use of

UC between the first and second experiments is similar. However, by exogeneously imposing the use of UC on superiors, the first experiment could not clearly distinguish whether superiors differed in their use of UC to control their temptation (even though there may have been large differences in behavior).

23 Allowing endogenous choice, as in our second experiment, afforded a better understanding of the use of UC.

5.3 Binding commitments in EC

23 We observed, ex post, that some superiors had acceptance rates that greatly differed from the average. For example, four EXO superiors accepted less than 25% of high proposals. But with this type of “fishing,” one cannot distinguish between random and systematic occurrences. By using superiors’ choices to classify them ex ante in EC and then testing for differences in acceptance rates, we can conclude that there is some systematic difference between superiors’ use of UC. In addition, behavior can differ due to being assigned to use UC versus choosing to use UC.

21

Table 7 presents data on the frequency distribution of unobservable commitments in the EC treatment, by superior type. The extremely lenient commitments are concentrated in the group who preferred UC in Panel B (71.4% of the UCpref superiors’ commitments are above 194, versus 21.1% of the nopref superiors’ commitments). Further, 43.6% of the commitments by the UCpref superiors were for 200, indicating that they would accept any project, even those that yielded them no profits. The strict

(<170) commitments are concentrated in the nopref group in Panel C (56% of their commitments are

<170, compared to 11% of the UCpref superiors’ commitments).

24 The UCpref group’s mean commitment of 189.8 is significantly greater than the nopref group’s 166.2 (two-tailed p < 0.01). These results parallel those of the acceptance rates: superiors who preferred to use UC set extremely high commitment levels that caused them to accept a high percentage of high proposals.


5.4 Funding requests for EC (H8)

In the first experiment, subordinates made funding requests such that they maximized their profits conditional on superiors’ acceptance behavior. Since, on average in EC, the acceptance rates are similar between EC-UC and EC-NC and increasing over rounds for both, we would expect to observe (1) no difference in request levels between UC and NC and (2) an increase in request levels over time of approximately the same magnitude for both UC and NC.

We estimate the same model as in experiment 1, for costs above 100, given in (6):

Expected Request | High Cost = 126.77 – 1.71 (NC/UC) + 1.71 (Costsq) – 0.00 (NBA) + 1.39 (Round)

+ 0.16 (NC/UC*Round). (6)

As predicted, the NC/UC and NC/UC*Round coefficients are both not significant (p’s > 0.70) and the

Round coefficient is significantly positive (p < 0.05). In addition, the coefficient on Costsq is significant

(p < 0.001) and of about the same magnitude as in the first experiment. H8 is not rejected; there is no difference in requests for EC-NC and EC-UC subordinates.

24 Commitments by the nopref superiors become significantly more lenient in the second half.

22

Unlike the first experiment, however, the non-binding announcement appears to have virtually no effect on the subordinates’ requests (

NBA coefficient in (6) = –0.00), at least when cost is high and NC and UC are pooled. To investigate further, we estimated the following models for costs under 101 and costs 101 and higher:

Expected Request | Low Cost = 124.29 – 23.10 (NC/UC) + 1.68 (Costsq) + 0.05 (NBA) + 2.48 (Round)

+ 0.15 (NC/UC*NBA) (7′)

Expected Request | High Cost = 133.93 – 11.15 (NC/UC) + 1.71 (Costsq) – 0.07 (NBA) + 1.49 (Round)

+ 0.10 (NC/UC*NBA), (7′′) where variables are as previously defined. Coefficients on Costsq and Round are positive and significant, as expected.

Three of the four NBA coefficients implied by these models are positive (the negative coefficient,

-0.07, is for NC in the high-cost region and it is not significant), but only one is significant (the 0.20 coefficient for UC in the low-cost region, p < 0.05).

25 This general lack of association between nonbinding announcements and funding requests is contrary not only to the findings in the first experiment, but also to Rankin et al.’s (2003) results. We speculate that in the EC treatment, subordinates are focused on the superior’s choice of decision method and pay smaller attention to the non-binding announcement conditional on the superior not choosing unobservable commitment. The coefficient of -23 on NC/UC indicates a very large difference (although significant only at two-tailed p < 0.14) in the subordinates’ behavior conditional on superiors’ decision choice, but the 0.15 coefficient on interaction term has a countervailing effect. Therefore, for a non-binding announcement of 100 and a low cost draw, our expectation is an 8 point lower request if a superior chooses unobservable commitment. (The lower requests from subordinates is one factor contributing to lower subordinate earnings when the superior chooses UC; see Table 4).

25 Similar models for experiment 1 indicate that all four NBA coefficient are positive (and generally significant: p’s

< 0.10, except for UC in the high-cost region, where p > 0.40).

23

5.5 Superiors’ earnings in EC

Table 4 shows superiors’ earnings for EC-NC and EC-UC to be approximately the same in the first half (43.3 and 44.0 for NC and UC, resp.) and in the second half (34.7 and 33.1, resp.), with earnings declining for both NC and UC. A repeated-measures model regressing superior earnings on NC/UC ,

Round (i.e., round-pairs), and NC/UC*Round shows no significant differences for either of the NC/UC related variables, but a significant Round effect (coef = -1.73, p < 0.03 for NC and -2.43, p < 0.01 for

UC), indicating that superior earnings decreased for both choices over time at approximately the same rate. These results parallel those in experiment 1: earnings do not significantly differ between superiors choosing UC and NC. These results also hold if we perform analyses by superior-type.

5.6 Subordinates’ earnings in EC (H10)

Instead, the different uses of UC substantially affected subordinate earnings. Table 8 shows that subordinates related to nopref superiors who chose UC had average earnings of 40.4, compared to 62.3 when the superior chose NC. For superiors who preferred UC, the effect was the opposite: subordinate earnings were 52.1 when UC was chosen versus 39.5 when NC was chosen. The model in (8), controlling for cost, 26 describes the behavior:

Expected Subordinate Earnings = 123.13 – 15.52 (NC/UC) – 12.56 (suptype) – 0.66 (Cost)

+ 26.08 (NC/UC*suptype), (8) where suptype = 0 for nopref superiors, 1 for UCpref superiors; and all other variables are as defined previously. The NC/UC*suptype effect is strongly significant (p < 0.001), indicating that the relation between the choice of NC or UC differs for types of superiors. Specifically, for nopref superiors,

26 We do not include a variable for Round in this model because for the UCpref superiors there is only one observation in the second half for which NC was chosen. This is likely not too much of a concern, because Table 8 shows that in the second half for UCpref superiors, subordinate earnings were extremely high when UC was chosen, which is consistent with the first half.

24

choosing UC results in 15.52 less in subordinate earnings (p < 0.001), whereas for UCpref superiors, choosing UC results in 10.56 more in subordinate earnings (p < 0.05).

27

This result is consistent with the acceptance analyses in which UCpref superiors appeared to use the UC device to enable them to accept almost any proposal, whereas the nopref group tended to use the

UC device to control their acceptance of “unfair” requests. It appears, however, that neither use of UC benefitted the superiors (relative to not using unobservable commitment), as superior earnings were about the same with either use of UC or using NC.

5.7 Non-binding announcements for EC (H11)

We parallel the first experiment’s analysis and estimate the effect of NBA on binding commitment when the superiors choose UC, given in (9):

Expected Binding = 172.87 – 0.08 (NBA) + 1.59 (Round) + 0.01 (NBA*Round). (9)

Although the NBA coefficient is negative, consistent with the “posturing” behavior noted in the first experiment, it is not significant (p > 0.70). In fact, no coefficient is significant.

However, because nopref and UCpref superiors utilize the UC device differently, we estimate separate models, as follows, for nopref and UCpref superiors, resp.:

Expected Binding = 142.03 + 0.08 (NBA) + 7.21 (Round) – 0.04 (NBA*Round) (9′)

Expected Binding = 157.35 + 0.28 (NBA) + 2.50 (Round) – 0.01 (NBA*Round), (9′′)

The NBA coefficients are positive for both types, but only significantly so (p < 0.08) for the nopref superiors, which suggests no posturing. However, the strong negative coefficient on NBA*Round for the nopref model indicates that posturing may be occurring in the later rounds for nopref superiors. Further tests reveal that for the nopref superiors in EC, the average effect of NBA across all rounds is significantly negative (p < 0.02), without a significant time trend. Thus, nopref superiors engaged in posturing and it

27 If we ignore superior-type (as in Table 4), we would draw the misleading inference that choice of UC leads to lower subordinate earnings (46.6 for UC versus 56.5 for NC, p < 0.03, after controlling for cost and round). By considering superior-type, we discover that this effect obtains only for superiors who have a strong preference for

UC and in fact, the opposite effect exists for superiors who exhibit no preference.

25

increased, but not significantly, over the rounds. For the UCpref superiors, posturing did not occur, as the effect on binding of an increase in NBA was positive over all rounds.

28 Finally, considering all superiors in EC, the posturing was not significant and did not change over rounds. One way to view this is to consider the nopref superiors as those most caring about not being taken advantage of. When they used a more generous unobservable commitment, they balanced it with a harsher non-binding announcement.

Perhaps in the (vain) hope that they would not receive a request at the limit of their generosity.

As an analogous test for the NC choices, we used a binary dependent variable, whether a request was accepted, in a logit model with the same explanatory variables with the addition of a variable for request, similar to the first experiment’s analysis. The coefficient on NBA is positive (0.03, p < 0.05), and the coefficient on NBA*Round is negative (-0.004, p < 0.04). This combination of coefficients indicates that in EC-NC, no posturing was occurring in early rounds, and although it started to appear in later rounds, the amount of posturing was minuscule (i.e., not significant).

6. Conclusion

We investigate the role of unobservable commitment in management control. In theory, unobservable commitments should have no effect on behavior and should not be preferred over the standard iterated response decision mode. In contrast we find superiors using unobservable commitments choose the wealth-maximizing strategy more often than without unobservable commitment as well as more often than normally seen in structurally similar games. What is particularly striking is the willingness of superiors to make unobservable commitments to accept exceptionally low earnings, while superior’s behavior in the no commitment treatment is roughly similar to responder behavior in generic bargaining games. We also find that when given the choice superiors choose unobservable commitment about 70% of the time, in contrast to several recent experiments which use structurally similar games, but without private information. We conjecture that the information asymmetry may have exacerbated the

28 For UCpref, the slope is not significant, nor is the average NBA effect across all rounds (both p’s > 0.40).

26

tendency seen in prior experiments to display more concern for wealth maximization and less concern for fairness when choosing strategies before knowing others’ moves, because information asymmetry cause fairness judgments to become more difficult.

When superiors were able to choose their decision method, there were some superiors who used the unobservable commitment to lock into rejecting high requests from subordinates. Therefore there is heterogeneity with respect to the use of unobservable commitment, with some superiors using unobservable commitment in the spirit of a commitment device. Perhaps we should not be surprised at this result; some workers use retirement savings vehicles to lock in sufficient retirement savings, yet in general economists believe workers lock in to far too low savings rates.

We also observe an odd relationship between the non-binding announcements and unobservable commitment. First the non-binding announcements are extremely harsh, which probably decreases their credibility. The unobservable commitments, whatever their purpose, are clearly not used to lock into the unrealistically harsh non-binding announcements. Second, superiors, especially when obligated to use unobservable commitment, resort to posturing, that is not only do they abandon their non-binding announcements but they actual send more aggressive non-binding announcements to accompany more acquiescent unobservable commitments. Further investigation is likely warranted, including perhaps a specially designed questionnaire and within-participant observations. We do not observe nearly as much posturing when superiors are given the choice of decision mode.

In many models, commitment plays an integral role in the solution to agency problems. Yet commitment, at least of the degree often assumed in agency models, is rarely observed in practice.

Therefore, effective alternatives for full, observable commitment are clearly of value. However, our evidence indicates that unobservable commitment is not efficacious, at least in our setting, and possibly should be avoided. In fact, it seems better for superiors to let their emotions have “free rein”, if their goal is to convince subordinates of their willingness to retaliate against them for their unfair behavior.

27

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Oxoby, R., and K. McLeish. 2004. Sequential decision and strategy vector methods in ultimatum bargaining: evidence on the strength of other-regarding behavior. Economic Letters 84: 399-405.

Paulsen, A. and M. Roos. 2010. Do people make strategic commitments? Evidence on strategic information avoidance. Experimental Economics.

13(2): 206-225.

Paulsen, A. and J. Tan. Information acquisition in the ultimatum game: An experimental study.

Experimental Economics . 9(3): 281-297.

Poterba, J. 1995. Balanced budget rules and fiscal policy: Evidence from the states. National Tax Journal.

48(3): 329-336.

Rankin, F., Schwartz, S., and R. Young. 2003. Management control using nonbinding budgetary commitments. Journal of Management Accounting Research 15: 75-93.

_________, __________, and __________. 2008. The effect of honesty preferences and superior authority on budget proposals. The Accounting Review (July): 1083-1099.

Rapoport, A., and J. Sundali. 1996. Ultimatums in two-person bargaining with one-sided uncertainty:

Offer games. International Journal of Game Theory 25: 475-494.

Schmitt, P. 2004. On perceptions of fairness: The role of valuations, outside options, and information in ultimatum bargaining games. Experimental Economics 7: 49-73.

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Wirtschaftsforschung : 136-168.

Vanberg, C., 2008. Why do people keep their promises? An experimental test of two explanations.

Econometrica 76: 1467-1480.

Winter, E., and S. Zamir. 2005. An experiment with ultimatum bargaining in a changing environment.

The Japanese Economic Review 56 (3): 363-385.

29

Zeger, S., and K. Liang. 1986. Longitudinal data analysis for discrete and continuous outcomes.

Biometrics 42:121-130.

30

FIGURE 1

Percent of High Funding Requests (> 179) Accepted, by Treatments UC and NC and Round

90

80

70

60

50

40

30

20

10

0

1,2 3,4 5,6 7,8 9,10 11,12 13,14 15,16 17,18 19,20 round

NC [-1.45] UC [4.73]

NC = No Commitment UC = Unobservable Commitment

Slope coefficients based on OLS are in brackets.

31

FIGURE 2

Frequency of High Funding Requests (> 179), by Treatments NC and UC and Round

25

20

15

10

5

0

1,2 3,4 5,6 7,8 9,10 11,12 13,14 15,16 17,18 19,20 round

NC [0.22] UC [1.24]


Slope coefficients based on OLS are in brackets.

Each subordinate made one request per round, so the maximum number of requests > 179 is 38 for two rounds.

MODIFY this figure to have y-axis the % of requests > 179 to be comparable to experiment 2. This will involve changing the slope coeff also. [see next page]

32

New Figure 2—but will have to mess with formatting

60

50

40

30

20

10

0

1,2 3,4 5,6 7,8 9,10 11,12 13,14 15,16 17,18 19,20 round

NC [0.57] UC [3.25]

33

Figure 3B Acceptance rates for high requests (> 179) for EC, by superior type

100

90

80

70

60

50

40

30

20

Ucpref-UC [0.28]

Nopref-UC [3.15]

Nopref-NC [5.58]

10

0

34

FIGURE 4

Acceptance Rates for Low and High Funding Requests when Unobservable Commitment is Used—All

Rounds

100

90

80

70

60

50

40

30

20

10

0

ENDO-all

ENDO-no pref

ENDO-UC pref

EXO-UC imposed

< 180 > 179

Funding request

35

FIGURE 4 [CHOOSE BETWEEN ALL ROUNDS AND SECOND HALF]

Acceptance Rates for Low and High Funding Requests when Unobservable Commitment is Used—

Second Half

100

40

30

20

10

0

60

50

90

80

70

ENDO-all

ENDO-no pref

ENDO-UC pref

EXO-UC imposed

< 180 > 179

Funding request

36

TABLE 1

Summary Statistics for treatments NC and UC

Frequency Cost

All Rounds: Rounds 1 - 20

Request Intended Binding

NC

UC

380

380

100.4

102.5

(56.2)

100.4

102.5

(56.2)

158.6

165.0

(28.6)

159.5

165.0

(30.8)

83.2

80.0

(36.6)

82.7

75.0

(34.2)

N/A

N/A

(N/A)

183.8

195.0

(24.1)

NC

Frequency

190

UC 190

Cost

95.9

96.0

(55.5)

95.9

96.0

(55.5)

Half 1: Rounds 1 - 10

Request Intended Binding

153.3

160.0

(31.3)

151.6

150.0

(33.2)

84.1

80.0

(33.2)

86.9

85.0

(39.1)

N/A

N/A

(N/A)

179.7

195.0

(27.3)

Accepted Superior

79.0%

Earnings

37.4

80.5%

37.8


80.0%

Earnings

42.2

42.6

(8.9)

80.5%

45.4

43.7

(13.3)

Subord.

Earnings

49.3

48.6

Subord.

Earnings

49.8

53.1

(17.7)

44.6

42.5

(17.4)

NC

UC

Frequency

190

190

Cost

104.9

103.0

(56.6)

104.9

103.0

(56.6)


Request

163.9

170.0

(24.7)

167.4

174.0

(26.1)

Intended Binding

82.4

75.0

(39.9)

78.6

75.0

(27.9)

N/A

N/A

(N/A)

187.9

195.5

(19.7)


77.9%

Earnings

32.5

32.8

(7.0)

80.5%

30.1

30.0

(8.3)

Subord.

Earnings

48.9

49.5

(15.9)

52.6

54.2

(20.3)

Cost

Prediction under observable commitment

Request Intended Binding Accepted Superior

Earnings

50.0% 50.0

Subord.

Earnings

25.0 Obs. Comm.

100.0 100.0 N/A 100.0

NC = No Commitment; UC = Unobservable Commitment; Obs. Comm. = Observable Commitment.

Cell entries are mean, median, (standard deviation).

Frequency = number of observations (for superior and subordinate earnings, there are 19 observations).

Cost = actual cost.

Request = amount of funding requested by the subordinate.

Intended = intended funding limit (non-binding announcement) announced by the superior.

Binding = unobservable (binding) commitment to the funding limit made by the superior.

Accepted = percent of projects accepted.

Superior Earnings = superior earnings from project, calculated as (200 – Request).

Subord. Earnings = subordinate earnings from project, excluding 25-point endowment, calculated as

(Request – Cost).

37

NC

UC

NC

UC

NC

UC

TABLE 2

Rates of Acceptance for Various Levels of Funding Requests, by Treatment and Half

NC

UC

NC

UC

NC

UC

Request Level

Below 180 Above 179

All Rounds

Breakdown of Above 179

180 to 189 Above 189

0.892

0.925

0.467

0.570

0.750

0.789

0.159

0.421

Half One

0.887

0.923

0.475

0.447

0.882

0.737

0.174

0.250

Half Two

0.899

0.927

0.462

0.642

0.677

0.818

0.143

0.521


Cell entries are rates of acceptance for the given level of funding request.

*number of observations is less than 10.

TABLE 2 [with number of obs—decide if like better than above table 2]

Rates of Acceptance for Various Levels of Funding Requests, by Treatment and Half

Request Level

Below 180 Above 179


All Rounds

180 to 189 Above 189

0.892

0.925

43/92 = 0.467

73/128 = 0.570

36/48 = 0.750

41/52 = 0.789

7/44 = 0.159

32/76 = 0.421

0.887

0.923

0.899

0.927

Half One

19/40 = 0.475 15/17 = 0.882

21/47 = 0.447 14/19 = 0.737

Half Two

24/52 = 0.462

52/81 = 0.642

21/31 = 0.677

27/33 = 0.818

4/23 = 0.174

7/28 = 0.250

3/21 = 0.143

25/48 = 0.521

38

TABLE 3

Relative Frequency Distributions and Descriptive Statistics for Binding Commitment in UC Treatment

All rounds

Relative Frequency Distribution

< 170 170 - 179 180 - 189 190 - 194 195 - 199 200

.168 .118 .108 .045 .229

Descriptive Statistics

Mean Median Std. Dev.

.332 183.8 188.5 16.5

1st half

2nd half

.242 .126

.095 .111

.079

.137

.042

.047

.189

.268

.321 179.7

.342 187.9

185.3

190.2

16.6

11.4

Cell entries for the relative frequency distributions are the proportions of the 380 (190 per half) unobservable binding commitments made by UC superiors that fall into the given ranges. Descriptive statistics are for the binding commitments by individual superior (19 observations); thus, the medians and standard deviations differ from those reported in Table 1.

39

TABLE 4

Summary Statistics for treatments EC

Frequency Cost



EC-NC

EC-UC

122

[30.5%]

278

[69.5%]

94.6

96.5

(52.7)

102.6

103.0

(57.7)

159.0

160.0

(25.1)

157.7

158.5

(28.9)

98.7

100.0

(26.2)

97.7

100.0

(25.6)

N/A

N/A

(N/A)

180.0

192.5

(24.2)

84.4%

79.1%

Earnings

39.0

38.5

EC-NC

EC-UC

Frequency

62

[31.0%]

138

[69.0%]

Cost

94.8

98.0

(54.0)

95.0

88.5

(57.1)



153.5

155.0

(26.1)

102.1

100.0

(25.1)

N/A

N/A

(N/A)

83.9%

Earnings

43.3

151.1

150.0

(28.5)

100.4

100.0

(26.9)

174.7

185.0

(27.0)

78.2%

44.0

Subord.

Earnings

56.5

46.6

Subord.

Earnings

52.4

44.6

EC-NC

EC-UC

Frequency

60

[30.0%]

140

[70.0%]

Cost

94.3

96.0

(51.8)

110.1

123.5

(57.6)



164.7

163.5

(22.9)

95.1

100.0

(27.0)

N/A

N/A

(N/A)

85.0%

Earnings

34.7

164.3

165.0

(27.8)

95.1

100.0

(24.1)

185.2

199.0

(19.7)

80.0%

33.1

Subord.

Earnings

60.7

48.5

Prediction under observable commitment

Cost

100.0


Earnings

100.0 N/A 100.0

50.0% 50.0

Subord.

Earnings

25.0 Obs. Commitment

EC–NC = Endogenous Choice, Superior made no commitment; EC–UC = Endogenous Choice,

Superior made unobservable commitment; Obs. Commitment = Observable Commitment

Cell entries are mean, median, (standard deviation).

Frequency = number of observations (for superior and subordinate earnings, there are 20 observations).

Cost = actual cost.

Request = amount of funding requested by the subordinate.

Intended = intended funding limit (non-binding announcement) announced by the superior.

Binding = unobservable (binding) commitment to the funding limit made by the superior.

Accepted = percent of projects accepted.

Superior Earnings = superior earnings from project, calculated as (200 – Request).

Subord. Earnings = subordinate earnings from project, excluding 25-point endowment, calculated as

(Request – Cost).

40

TABLE 4-Panel B [DECIDE IF WANT; if so then can get rid of table 8]

Summary Statistics for treatments EC—superiors with no preference

Frequency Cost



71

[39.4%] 84.5%

Earnings

38.6

EC-No

Comm

EC-

Comm

109

[60.6%]

91.5

91.0

(54.5)

101.1

104.0

(58.4)

159.4

162.0

(26.8)

156.7

159.0

(28.6)

102.4

101.0

(23.2)

103.3

100.0

(25.6)

N/A

N/A

(N/A)

167.3

160.0

(22.3)

64.2%

36.5

EC-No

Comm

EC-

Comm

Frequency

32

[35.6%]

58

[64.4%]

Cost

86.7

73.0

(58.4)

88.6

80.0

(56.9)



153.0

155.0

(29.9)

149.7

150.0

(27.2)

108.1

102.5

(16.7)

109.3

103.0

(24.2)

N/A

N/A

(N/A)

160.7

151.0

(29.1)

78.1%

65.5%

Earnings

42.8

41.8

Frequency

EC-No

Comm

EC-

Comm

9 superiors

39

[43.3%]

51

[56.7%]

Cost

95.4

96.0

(51.5)

115.4

138.0

(57.4)



164.7

165.0

(23.1)

97.7

101.0

(26.7)

N/A

N/A

(N/A)

89.7%

Earnings

35.1

164.7

175.0

(28.4)

96.3

100.0

(25.6)

174.8

175.0

(22.5)

62.8%

30.5

Subord.

Earnings

62.3

40.4

Subord.

Earnings

59.4

43.5

Subord.

Earnings

64.8

36.9

41

TABLE 4-Panel C [DECIDE IF WANT]

Summary Statistics for treatments EC—superiors with UC preference

Frequency Cost



17

[9.4%] 88.2%

Earnings

39.2

EC-No

Comm

EC-

Comm

163

[90.6%]

107.0

114.0

(35.0)

103.9

103.0

(58.1)

158.3

160.0

(19.8)

158.2

155.0

(29.2)

103.8

100.0

(36.5)

93.5

99.0

(25.2)

N/A

N/A

(N/A)

189.8

199.0

(20.3)

90.8%

40.4

EC-No

Comm

EC-

Comm

Frequency

16

[17.8%]

74

[82.2%]

Cost

107.6

115.0

(36.1)

100.0

96.5

(58.5)



155.8

159.5

(17.3)

151.0

150.0

(29.6)

102.5

100.0

(37.2)

92.5

95.0

(27.4)

N/A

N/A

(N/A)

188.8

199.0

(25.2)

93.8%

91.9%

Earnings

41.6

47.5

Frequency

EC-No

Comm

EC-

Comm

9 superiors

1

[1.1%]

89

[98.9%]

Cost

97.0

97.0

(na)

107.0

103.0

(57.8)



199.0

199.0

(na)

125.0

125.0

(na)

N/A

N/A

(N/A)

0.0%

Earnings

0.0

164.1

165.0

(27.6)

94.4

100.0

(23.3)

191.2

199.0

(15.1)

89.9%

34.6

Subord.

Earnings

39.5

52.1

Subord.

Earnings

41.9

48.4

Subord.

Earnings

0.0

55.2

42

TABLE 4-Panel D

Summary Statistics for treatments EC—superiors with NC preference

Frequency Cost



34

[85.0%] 82.4%

Earnings

40.0

EC-No

Comm

EC-

Comm

6

[15.0%]

94.8

96.0

(56.5)

94.8

102.5

(38.2)

158.5

155.0

(24.5)

164.8

173.0

(28.4)

88.3

96.0

(23.8)

111.2

110.0

(13.9)

N/A

N/A

(N/A)

144.3

144.5

(11.1)

33.3%

22.7

EC-No

Comm

EC-

Comm

Frequency

14

[70.0%]

6

[30.0%]

Cost

98.9

109.0

(60.6)

94.8

102.5

(38.2)



152.1

144.5

(26.9)

164.8

173.0

(28.4)

88.0

96.0

(19.6)

111.2

110.0

(13.9)

N/A

N/A

(N/A)

144.3

144.5

(11.1)

85.7%

33.3%

Earnings

46.4

22.7

Frequency

EC-No

Comm

EC-

Comm

2 superiors

20

[100.0%]

0

[0.0%]

Cost

94.3

96.0

(51.8)

NA



163.0

160.0

(22.2)

88.5

95.0

(26.9)

N/A

N/A

(N/A)

80.0%

Earnings

35.6

NA NA NA NA NA

Subord.

Earnings

52.7

8.2

Subord.

Earnings

48.4

8.2

Subord.

Earnings

55.8

NA

43

TABLE 5

Rates of Acceptance for Various Levels of Funding Requests, by Treatment and Half for EC

EC-NC

EC-UC

EC-NC

EC-UC

EC-NC

EC-UC

Request Level

Below 180 Above 179

All Rounds


180 to 189 Above 189

0.966

0.896

0.529

0.558

0.786

0.667

0.350

0.491

Half One

0.939

0.869

0.462

0.484

0.667*

0.600

0.286*

0.375

Half Two

1.000

0.929

0.571

0.600

0.875*

0.722

0.385

0.541

EC-NC = Endogenous choice, choosing not to make a commitment

EC-UC = Endogenous choice, choosing to make an unobservable binding commitment

Cell entries are rates of acceptance for the given level of funding request.

*number of observations is less than 10.

Cell sizes for above [probably not include in paper]

EC-NC

EC-UC

EC-NC

EC-UC

EC-NC

EC-UC

Request Level

Below 180 Above 179

All Rounds


180 to 189 Above 189

88

192

34

86

14

33

20

53

49

107

39

85

13

31

21

55

Half One

Half Two

6

15

8

18

7

16

13

37

44

EC-NC

EC-UC

EC-NC

EC-UC

EC-NC

EC-UC

EC-NC

EC-UC

TABLE 6

Rates of Acceptance for Low and High Funding Requests, by Treatment and Superior Preference in EC—

All Rounds

EC-NC

EC-UC

EC-NC

EC-UC

EC-NC

EC-UC

EC-NC

EC-UC

Below 180

Request Level

Above 179 All

No Strong Preference (9 superiors)

0.958

0.831

Strong Preference for UC (9 superiors)

0.933 0.500* 0.882

0.955 0.808 0.908

Strong Preference for NC (2 superiors)

1.000 0.333* 0.824

0.500* 0.000* 0.333*

0.966

0.896

* number of observations is less than 10.

0.609

0.188

Totals (20 superiors)

0.529

0.558

0.845

0.642

0.844

0.791

Consider adding totals rows for each preference. Should we have panels for 1 st and 2 nd half (see following for what they look like)?

Above table with cell sizes—should strongly consider this one—or can use above table but mark with an asterisk those cells with sample sizes less than 10 (or 20).

Below 180

Request Level

Above 179 All


46/48 = 0.958 14/23 = 0.609 60/71 = 0.845

64/77 = 0.831 6/32 = 0.188 70/109 = 0.642


14/15 = 0.933 1/2 = 0.500 15/17 = 0.882

106/111 = 0.955 42/52 = 0.808 148/163 = 0.908


25/25 = 1.000 3/9 = 0.333 28/34 = 0.824

2/4 = 0.500 0/2 = 0.000 2/6 = 0.333


85/88 = 0.966 18/34 = 0.529 103/122 = 0.844

172/192 = 0.896 48/86 = 0.558 220/278 = 0.791

45

TABLE 6 – Panel A [DECIDE IF WANT ALL ROUNDS or by HALF or BOTH]


First Half

EC-NC

EC-UC

EC-NC

EC-UC

EC-NC

EC-UC

EC-NC

EC-UC

Below 180

Request Level

Above 179 All


0.913

0.783


0.933 1.000* 0.938

0.965 0.765 0.919


1.000 0.333* 0.857

0.500* 0.000* 0.333*

0.939

0.869


0.444*

0.167


0.462

0.484

0.781

0.655

0.839

0.783

Consider adding totals rows for each preference.


EC-NC

EC-UC

EC-NC

EC-UC

EC-NC

EC-UC

EC-NC

EC-UC

Below 180


21/23 = 0.913

36/46 = 0.783

11/11 = 1.000

2/4 = 0.500

Request Level

Above 179

4/9 = 0.444

2/12 = 0.167

1/3 = 0.333

0/2 = 0.000

All

25/32 = 0.781

38/58 = 0.655


14/15 = 0.933

55/57 = 0.965

1/1 = 1.000

13/17 = 0.765

15/16 = 0.938

68/74 = 0.919


12/14 = 0.857

2/6 = 0.333

46/49 = 0.939


6/13 = 0.462 52/62 = 0.839

93/107 = 0.869 15/31 = 0.484 108/138 = 0.783

46

TABLE 6 – Panel B [DECIDE IF WANT ALL ROUNDS or by HALF or BOTH]


Second Half

EC-NC

EC-UC

EC-NC

EC-UC

EC-NC

EC-UC

EC-NC

EC-UC

Below 180

Request Level

Above 179 All


1.000

0.903


IND* 0.000* 0.000*

0.944 0.829 0.899


1.000 0.333* 0.800

IND* IND* IND*

1.000

0.929


0.714

0.200


0.571

0.600

0.897

0.627

0.850

0.800

IND* = indeterminate because number of observations is 0.

Consider adding totals rows for each preference.


EC-NC

EC-UC

EC-NC

EC-UC

EC-NC

EC-UC

EC-NC

EC-UC

Below 180

Request Level

Above 179


25/25 = 1.000 10/14 = 0.714

39/39 = 1.000 12/21 = 0.571

All

35/39 = 0.897

28/31 = 0.903 4/20 = 0.200 32/51 = 0.627


0/0 = IND 0/1 = 0.000

51/54 = 0.944 29/35 = 0.829

0/0 = IND


0/1 = 0.000

80/89 = 0.899


14/14 = 1.000 2/6 = 0.333 16/20 = 0.800

0/0 = IND 0/0 = IND

51/60 = 0.850

79/85 = 0.929 33/55 = 0.600 112/140 = 0.800

47

TABLE 7

Relative Frequency Distributions and Descriptive Statistics for Binding Commitment in EC Treatment

Panel A—all superiors (n = 20)


< 170 170 - 179 180 - 189 190 - 194 195 - 199 200



All rounds

1st half

.306 .076

.428 .036

.076

.051

.043

.051

.209

.159

.291

.275

176.2

172.2

176.6

172.3

11.3

9.3

2nd half .186 .114 .100 .036 .257 .307 181.8 186.3

Cell entries for the relative frequency distributions are the proportions of the unobservable binding commitments made by UC superiors that fall into the given ranges. Descriptive statistics are for the binding commitments by individual superior (20 observations); thus, the medians and standard deviations differ from those reported in Table 4.

For “no preference” superiors (n = 9)

10.9

All rounds

1st half


< 170 170 - 179 180 - 189 190 - 194 195 - 199 200

.560

.690

.110

.069

.064

.086

2nd half .412 .157 .039

For “UC preference” superiors (n = 9)

.055

.069

.039

.119

.000

.255

.092

.086

.098



166.2

160.3

171.1

167.1

161.8

179.3

14.8

11.8

16.4

All rounds

1st half


< 170 170 - 179 180 - 189 190 - 194 195 - 199 200

.110 .055

.176 .014

.056 .090

.086

.027

.135

.037

.041

.034

.276

.297

.258



.436 189.8

.446 187.2

.427 191.3

189.8

185.9

192.6

7.8

6.7

5.9

2nd half

48

The role of commitment in resource allocation: A laboratory

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